Modeling of the combined dynamics of leptospirosis transmission and seroconversion in herds.

Leptospirosis is a zoonotic disease-causing illness in both humans and animals resulting in related economic impacts due to production loss as well as prevention and control efforts. Several mathematical models have been proposed to study the dynamics of infection but none of them has so far taken into account the dynamics of seroconversion. In this study, we have developed a general framework, based on the kinetic model for animal leptospirosis, that combines both the antibody (exposure marker) and infection dynamics to simultaneously follows both seroconversion and infection status of leptospirosis in a herd population. It is a stochastic compartmental model (for transition rates) with time delay (for seroconversion) which describes the progression of infection by a SEIRS (susceptible, exposed, infected, removed and susceptible) approach and seroconversion by four-state antibody kinetics (antibody negative and three antibody positive states of different antibody levels). The model shows that it is possible to assess and follow both seroconversion and infection status through the prism of diagnostic testing. Such an approach of combined kinetics could prove very useful to assist the competent authorities in their analyzes of epidemic situations and in the implementation of strategies for controlling and managing the associated risks.